### Video Transcript

Alice is randomly tossing shoes
onto her rug which is modelled in the diagram. What is the probability that the
shoes will land in the shaded area of the rug? Give your answer as a fraction in
its simplest form.

So in the diagram, what we can see
is we’ve got a rug, and the rug is eight foot by 16 foot. And within the rug, there’s a
shaded area which is four foot by 10 foot. So now, in order to work out what
probability that the shoe will land in the shaded area is, we need to work out what
fraction of the rug is shaded. And to do that, we’re gonna have to
work out the area of the rug and the area of the shaded section. And to do that, we’ve got a
formula. And that formula is that the area
of a rectangle is equal to the length multiplied by the width. So what I’m gonna do is call the
total area of the rug 𝐴 and the area of the shaded region 𝐵.

So, first of all, to work out the
area of the total rug, so the area of 𝐴, it’s gonna be equal to 16 multiplied by
eight. And that’s 16 foot multiplied by
eight foot which is gonna be equal to 128 square feet. And we could work that out mentally
because we could do 10 multiplied by eight which is 80. Six multiplied by eight which is
48. Add them together, gives us our
128. Okay, great, so we’ve got the total
area of the rug. Now, we need to move on and find
the area of the shaded region. So the area of the shaded region,
region 𝐵, is equal to 10 multiplied by four. That’s 10 foot multiplied by four
foot which is gonna be equal to 40 square feet.

So now, we’ve got the areas of both
the total rug and the shaded region. What we want to do is work out what
fraction of the rug is shaded. Because that’s gonna give us the
probability that the shoe will land in the shaded area of the rug. So, therefore, we can say that the
probability that the shoe is gonna land in the shaded area is gonna be equal to 40
divided by 128 or 40 over 128. And that’s because 40 was the area
of the shaded region. And 128 is the total area of the
rug. And we said that the fraction of
the rug that is shaded is gonna be the same as the probability that the shoes will
land in the shaded area. So have we finished? Have we solved the problem?

Well, if we take a look at the
question, it says that we want the answer as a fraction which we’ve got. So yes, we’ve done that. However, it’s not in its simplest
form. So we haven’t quite finished. We need to carry out another
stage. Well, in order to simplify the
fraction, what we wanna do is find a factor that goes into both 40 and 128. And what we’re really looking for
is the highest common factor. We can see that the highest common
factor of 40 and 128 is eight. And therefore, if we divide 40 by
eight, we get five. And we divide 128 by eight, we get
16.

Now, you might think, “Well, how
would I know that eight goes into both of these numbers?” Well, 40, we know that eight goes
into five times. And that’s quite straightforward
cause we should know that from our times tables. And if we refer back to the early
part of the question, we can see that we already worked out 16 multiplied by eight,
was 128. So therefore, we know that eight
goes into 128 16 times. So, therefore, we can say that the
probability that the shoes will land in the shaded area of the rug, as a fraction in
its simplest form, is equal to five over 16 or five-sixteenths.